Image Aliasing and Anti-aliasing

What is Pixelation?

Anti-aliasing is a powerful method to increase spatial resolution.
The method increases spatial resolution through luminance modulation.
The term is derived from Nyquist's sampling theorem.

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Yes, Okay... It's all about "Pixels" ("Picture Elements")

Everything in computer graphics starts with the simple fact that a computer screen is composed of tiny points of information called pixels. On a PC, the number of pixels on the screen is determined by the display mode or screen resolution of the user's computer system. The most common resolutions are 640 horizontal pixels x 480 vertical pixels,
800 by 600 and 1024 by 768 pixels. Because the screen resolution of a PC display is fixed, the number of pixels doesn't change, no matter how large a monitor screen is used. On larger screens, the dots just get larger. (On a Macintosh, the number of pixels per inch is fixed, so a larger monitor displays more pixels and actually lets you display more information.)

Computer screens don't have enough dots available to create small, complex shapes like letters. This can be especially noticeable in large fonts where diagonal lines are created with a stair-stepped appearance, sometimes called "the jaggies" or "pixelation."

The problem is overcome by using the technique known as anti-aliasing. Anti-aliasing causes the pixels along a diagonal border to be filled with a color that is in between the color of the letters and the color of the background (see below). The goal is to create an optical trick that fools the eye into seeing a smoother shape, especially at a distance.

The samples below show what's happening. The non-anti-aliased examples
break up curves into steps and jagged outcrops, sometimes called "the jaggies"
or "pixelation". This is what gives the letter its coarse appearance.
In the "anti-aliased" example ( see enlargement below ),
shades of gray have been substituted around the lines which would otherwise
be broken across a pixel.

Non-Anti-Aliased Image:

Anti-Aliased Image:

Non-Anti-Aliased Image:

Anti-Aliased Image:

Enlargements of the Images Above:

Non-Anti-Aliased Image:

Anti-Aliased Image:

Pixelation Enlargement:

Anti-aliased Graphic Enlargement:

Grande Anti-aliased Graphic Enlargement:

1
From Nyquist's sampling theorem, one cycle of a horizontal or vertical grating, having the maximum spatial frequency fmax that can be realised on a CRT, has a period of 2 pixels (it will not be sinusoidal). The required pixel size xp to achieve a specific fmax is thus given by:

xp = (p · d) / (360° · fmax), (1)

where d denotes the observer distance. At a typical reading distance of 40 cm for example, the required pixel size for a grating to be at the resolution limit of a young observer would be 0.12 mm. This is below the typical pixel size, or “dot pitch”, of current colour monitors which is around 0.25 mm (corresponding to 100 dpi). Thus, to reach the highest spatial frequency, the observer distance must be increased; based on the above, at least 80 cm distance are needed for a young observer, unless a monitor with smaller pixel size is available.

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